What is the best way to shunt these carriages so that each train
can continue its journey?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
How many different rhythms can you make by putting two drums on the
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many models can you find which obey these rules?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Use the clues to colour each square.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
An activity making various patterns with 2 x 1 rectangular tiles.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
These practical challenges are all about making a 'tray' and covering it with paper.
How many different triangles can you make on a circular pegboard that has nine pegs?
How many triangles can you make on the 3 by 3 pegboard?
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Can you find all the different ways of lining up these Cuisenaire
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Investigate the different ways you could split up these rooms so
that you have double the number.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?